(1) How do you start the tmux sessions? and
sftp within? (2) Do you really need multiple tmux sessions? One tmux session with one window with multiple panes may be enough. (3) When detached from tmux, does ps aux show the running tmux server and the sftp processes? (4) tmux -L allows you to work with a non-default tmux server. How exactly do you use it? Do you even use tmux -L to start the sessions is question in the first place? Please [edit] and post exact commands.